I sometimes get potions with poison in them (some negative effect).

Obviously I don't want to drink those, so how do I use those on enemies?

I mean, if I train in alchemy (haven't yet), how do I use poisons I've made? can I apply them to weapons? if so, how?
(btw, I play on xbox)

Yes you can apply them to weapons.

Another way to use them is to reverse pickpocket poisons into npcs with pockets (there is a perk in the pickpocket tree) to damage them.

Using a poion will coat your weapon rather than drink it.
Some potions have negative effects and using them will drink (the negative effects can be removed with perks).

how do I determine which weapon I coat with the poison? is it the equiped one?
what if it's an bow, will one arrow, or all arrows get coated?
can I do this long in advance?
will it affect once? or all targets while it's coated? will it be coated for a duration, or just for once hit?

It's the equipped weapon.
Just one arrow.
Yes.
Only once in my experience.

Yeah, only the next arrow you use will be poisoned. And the next strike that hits if you use a melee weapon... right?

I think there is a perk under alchemy that let you hit twice(your next 2 swing or shots) with the poison ,correct me if I'm wrong.

Nope, that's right. Concentrated Poison is the Perk.